Università di Roma “Tor Vergata”

Corso di Laurea Magistrale in Matematica


Algebraic Geometry

I Semester: 01/10/2018 - 21/12/2018 – 8 credits (64 hours)

Lecturer: Prof. Flaminio Flamini (flamini[ANTISPAM]@mat.uniroma2.it)

Lectures (course in English on demand)
Tuesday (Martedì)/14:00-16:00/Room 29A  – Wednesday (Mercoledì)/16:00-18:00/Room 29A/Friday (Venerdì)/11:00-13:00/Room 29A 
Office hour
Semester I: Tuesday (Martedì)/16:00-18:00 / office 1116 (please send an e-mail some days before).


· Tentative program

· Daily calendar of lectures

 · Lecture notes (preliminary version)

 · Proposed Exercises

 · Good to know: (i) Some topics in Commutative Algebra (used in the Algebraic Geometry course) will be treated in more depth in the course  Commutative Algebra 2018/19 taught by Prof. R. Schoof 

(ii) There will be some intersection (with a different perspective) with the course  Representation Theory 1 2018/19 taught by Prof.ssa M. Lanini 



Further Teaching Material (in alphabetic order)

·     M. Atiyah , I. G. Macdonald : Introduction To Commutative Algebra, Addison-Wesley Series in Mathematics(IN BIBLIOTECA)

·     F. Bottaccin: Introduzione alla Geometria Algebrica, 2010/11

·     C. Ciliberto : Drafts of “Algebraic Geometry” course

·      O. Debarre: Introduction à la géométrie algébrique,e, cours de DEA, 1999/2000, et M2, 2007/2008.

·      I. Dolgachev : Introduction to algebraic geometry, 2013

·      W. E. Fulton : Algebraic Curves. An introduction to algebraic geometry, 2008

·      A. Gathmann: Algebraic Geometry, Notes for a class taught at the University of Kaiserslautern, 2002/03

·      J. Harris : Algebraic geometry (a first course), Graduate Texts in Math. No. 133. Springer, New York-Heidelberg, 1977 (IN BIBLIOTECA)

·       R. Hartshorne : Algebraic Geometry, New York: Springer-Verlag, 1977. (IN BIBLIOTECA)

·       B. Hassett: Introduction to algebraic geometry, Cambridge University Press. 2007 (IN BIBLIOTECA)

·       K. Hulek: Elementary Algebraic Geometry, Student mathematical library, vol. 20. 2003 AMS

·       K. Kendig: "Elementary Algebraic Geometry", Dover Books on Mathematics, second edition, Dover Publications, 2015.

·       J. MIlne : Algebraic Geometry, Notes on-line

·       D. Mumford : "The Red Book of Varieties and Schemes", LNM 1358, Springer (IN BIBLIOTECA)

·       M. Reid : Undergraduate Algebraic Geometry, London Math. Soc. Student Texts, vol. 12, 1988, Cambridge University Press

·       I. Shafarevich : Basic Algebraic Geometry, I. Springer-Verlag, New York-Heidelberg, 1977. (IN BIBLIOTECA)

·       E. Sernesi : Private Notes "Algebraic Geometry Course".

·       E. Sernesi : "Appunti sui divisori speciali", typewritten handouts.

       ·       E. Sernesi : "Una breve introduzione alle curve algebriche", Nervi 1984: Scanned pdf and  translation in english (by C.Fontanari)

·      K. Ueno: An Introduction to Algebraic Geometry 1997.(IN BIBLIOTECA)

·      A. Verra : Introduzione alle curve algebriche piane, Alfaclass Summer School



About Algebraic Geometry


·         Geometria Algebrica

·         Algebraic Geometry

·         G. Castelnuovo

·         F. Enriques

·         G. Fano

·         A. Grothendieck

·         D. Hilbert

·         E. Noether

·         M. Noether

·          C. Segre

·          J.P. Serre

·          F. Severi

·          G. Veronese

·          A. Weil

·          O. Zariski


Exams/Learning aims

* Exam Oral examination


* Learning aims Our general scope is to present fundamental concepts related to the problem of solvings systems of polynomial equations. Algebraic Geometry studies these solutions from a “global” point of view, through the theory of Algebraic Varieties. We will define this important class of varieties and then we will study some of their most important properties and discuss key examples, which are fundamental for the whole theory. Learning aims are to give to students the following skills:

·         working knowledge of basic elements of affine/projective geometry, of homomorphisms, isomorphisms and rational maps among algebraic varieties;

·         familiarity with explicit examples, including plane curves, quadric surfaces, Grassmannian of lines, Veronese and Segre varieties, etc;

·         if time permits, familiarity with the rich geometry of the canonical curve in terms of special linear series.


Exams: date/room/hours

o 1o Exam: Venerdì 18 Gennaio 2019, ore 11:30, Aula: 29A

o 2o Exam: Martedì 26 Febbraio 2019, ore 09:30, Aula: 16

o 3o Exam: Mercoledì 12 Giugno 2019, ore 14:30, Aula: 16

o 4o Exam: Venerdì 28 Giugno 2019, ore 09:30, Aula: L3

o 5o Exam: Mercoledì 11 Settembre 2019, ore 15:00, Aula: 11

o 6o Exam: Giovedì 26 Settembre 2019, ore 09:30, Aula: 16


Past years

Prof. F. Flamini a.a.2017-2018

Prof. F. Flamini a.a.2016-2017

Prof. G. Pareschi a.a.2015-2016

Prof. F. Flamini a.a.2014-2015

Prof. G. Pareschi a.a.2012-2013

Prof. C. Ciliberto a.a.2010/11 & 2011/12

Prof.ssa F. Tovena a.a.2009-2010